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Simplifying (3x + -4) * 2 + -1(5x + -2)(5x + 2) + 20 = 0 Reorder the terms: (-4 + 3x) * 2 + -1(5x + -2)(5x + 2) + 20 = 0 Reorder the terms for easier multiplication: 2(-4 + 3x) + -1(5x + -2)(5x + 2) + 20 = 0 (-4 * 2 + 3x * 2) + -1(5x + -2)(5x + 2) + 20 = 0 (-8 + 6x) + -1(5x + -2)(5x + 2) + 20 = 0 Reorder the terms: -8 + 6x + -1(-2 + 5x)(5x + 2) + 20 = 0 Reorder the terms: -8 + 6x + -1(-2 + 5x)(2 + 5x) + 20 = 0 Multiply (-2 + 5x) * (2 + 5x) -8 + 6x + -1(-2(2 + 5x) + 5x * (2 + 5x)) + 20 = 0 -8 + 6x + -1((2 * -2 + 5x * -2) + 5x * (2 + 5x)) + 20 = 0 -8 + 6x + -1((-4 + -10x) + 5x * (2 + 5x)) + 20 = 0 -8 + 6x + -1(-4 + -10x + (2 * 5x + 5x * 5x)) + 20 = 0 -8 + 6x + -1(-4 + -10x + (10x + 25x2)) + 20 = 0 Combine like terms: -10x + 10x = 0 -8 + 6x + -1(-4 + 0 + 25x2) + 20 = 0 -8 + 6x + -1(-4 + 25x2) + 20 = 0 -8 + 6x + (-4 * -1 + 25x2 * -1) + 20 = 0 -8 + 6x + (4 + -25x2) + 20 = 0 Reorder the terms: -8 + 4 + 20 + 6x + -25x2 = 0 Combine like terms: -8 + 4 = -4 -4 + 20 + 6x + -25x2 = 0 Combine like terms: -4 + 20 = 16 16 + 6x + -25x2 = 0 Solving 16 + 6x + -25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. -0.64 + -0.24x + x2 = 0 Move the constant term to the right: Add '0.64' to each side of the equation. -0.64 + -0.24x + 0.64 + x2 = 0 + 0.64 Reorder the terms: -0.64 + 0.64 + -0.24x + x2 = 0 + 0.64 Combine like terms: -0.64 + 0.64 = 0.00 0.00 + -0.24x + x2 = 0 + 0.64 -0.24x + x2 = 0 + 0.64 Combine like terms: 0 + 0.64 = 0.64 -0.24x + x2 = 0.64 The x term is -0.24x. Take half its coefficient (-0.12). Square it (0.0144) and add it to both sides. Add '0.0144' to each side of the equation. -0.24x + 0.0144 + x2 = 0.64 + 0.0144 Reorder the terms: 0.0144 + -0.24x + x2 = 0.64 + 0.0144 Combine like terms: 0.64 + 0.0144 = 0.6544 0.0144 + -0.24x + x2 = 0.6544 Factor a perfect square on the left side: (x + -0.12)(x + -0.12) = 0.6544 Calculate the square root of the right side: 0.808949937 Break this problem into two subproblems by setting (x + -0.12) equal to 0.808949937 and -0.808949937.Subproblem 1
x + -0.12 = 0.808949937 Simplifying x + -0.12 = 0.808949937 Reorder the terms: -0.12 + x = 0.808949937 Solving -0.12 + x = 0.808949937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.12' to each side of the equation. -0.12 + 0.12 + x = 0.808949937 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + x = 0.808949937 + 0.12 x = 0.808949937 + 0.12 Combine like terms: 0.808949937 + 0.12 = 0.928949937 x = 0.928949937 Simplifying x = 0.928949937Subproblem 2
x + -0.12 = -0.808949937 Simplifying x + -0.12 = -0.808949937 Reorder the terms: -0.12 + x = -0.808949937 Solving -0.12 + x = -0.808949937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.12' to each side of the equation. -0.12 + 0.12 + x = -0.808949937 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + x = -0.808949937 + 0.12 x = -0.808949937 + 0.12 Combine like terms: -0.808949937 + 0.12 = -0.688949937 x = -0.688949937 Simplifying x = -0.688949937Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.928949937, -0.688949937}
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